Question

A famous relation in physics relates ‘moving mass’ m to the ‘rest mass’ m₀ of a particle in terms of its speed v and the speed of light, c. (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant c. He writes:

`m = m_0/(1-v^2)^(1/2)`

Guess where to put the missing c.

Answer 1

From the given equation, `m_0/m = sqrt(1-v^2)`

Left hand side is dimensionless

Therefore, right hand side should also be dimensionless.

It is possible only when `sqrt(1-v^2)  "should be" sqrt(1-v^2/c^2)`

Thus the correct formula is m = `m_0 (1 - v^2/c^2)^((-1)/2)`